Related papers: Numerical integration for ab initio many-electron …
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z \alpha is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a…
We study the Green's function of the $ \nu=1/2 $ Chern-Simons system in the temporal (Weyl) gauge. We derive the Chern-Simons path integral in the temporal gauge. In order to do this, we gauge transform the path integral in the Coulomb…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…
Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral.…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
We perform coupled-cluster and diffusion Monte Carlo calculations of the energies of circular quantum dots up to 20 electrons. The coupled-cluster calculations include triples corrections and a renormalized Coulomb interaction defined for a…
A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the…
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's…
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They…
We introduce a computationally efficient screening for the Coulomb potential that also allows calculating approximated long-range exact exchange contributions with an accuracy similar to an explicit full-range evaluation of the exact…
Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\Sigma$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
We present a molecular extension of our recently proposed Green's function embedding method, interacting-bath dynamical embedding theory (ibDET), for computing charged excitation energies at the $GW$ and EOM-CCSD levels. Starting from…
We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in…
We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and…
This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find…
We present a data-driven approach to mathematically model physical systems whose governing partial differential equations are unknown, by learning their associated Green's function. The subject systems are observed by collecting…